logos-blockchain-pocs/cryptarchia/slotless-cryptarchia.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3f485372-2531-4a49-8d15-5b26e9018a6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from dataclasses import dataclass\n",
    "from pyvis.network import Network\n",
    "from pyvis.options import Layout\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ea18f7d-34a8-4de8-b18f-e93329825840",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class Block:\n",
    "    id: int\n",
    "    t: float\n",
    "    height: int\n",
    "    parent: int\n",
    "    leader: int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cabf7946-8382-4102-b730-d74ed42ceb38",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class NetworkParams:\n",
    "    mixnet_delay_mean: int # seconds\n",
    "    mixnet_delay_var: int\n",
    "    broadcast_delay_mean: int # second\n",
    "    pol_proof_time: int # seconds\n",
    "\n",
    "    def sample_mixnet_delay(self):\n",
    "        scale = self.mixnet_delay_var / self.mixnet_delay_mean\n",
    "        shape = self.mixnet_delay_mean / scale\n",
    "        return np.random.gamma(shape=shape, scale=scale)\n",
    "    \n",
    "    def sample_broadcast_delay(self, blocks):\n",
    "        return np.random.exponential(self.broadcast_delay_mean, size=blocks.shape)\n",
    "\n",
    "    def block_arrival_time(self, block_time):\n",
    "        return self.pol_proof_time + self.sample_mixnet_delay() + self.sample_broadcast_delay(block_time) + block_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4e9df29f-fb4a-4dfb-a7b4-b8b4b0a6e6b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class Params:\n",
    "    CHAIN_HEIGHT: int\n",
    "    MEAN_BLOCK_TIME: int\n",
    "    honest_stake: np.array\n",
    "    adversary_control: float\n",
    "\n",
    "    @property\n",
    "    def N(self):\n",
    "        return len(self.stake)\n",
    "\n",
    "    @property\n",
    "    def stake(self):\n",
    "        if self.adversary_control:\n",
    "            adversary_stake = self.honest_stake.sum() / (1/self.adversary_control - 1)\n",
    "            return np.append(self.honest_stake, adversary_stake)\n",
    "        else:\n",
    "            return self.honest_stake\n",
    "    \n",
    "    @property\n",
    "    def relative_stake(self):\n",
    "        return self.stake / self.stake.sum()\n",
    "\n",
    "    def block_delay_at_height(self):\n",
    "        return np.random.exponential(self.MEAN_BLOCK_TIME / self.relative_stake, size=(self.CHAIN_HEIGHT, self.N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ced60818-fab2-49c4-9247-9a31047d40d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "params = Params(\n",
    "    CHAIN_HEIGHT=1000,\n",
    "    MEAN_BLOCK_TIME=20,\n",
    "    honest_stake = np.random.pareto(10, size=100),\n",
    "    adversary_control=None,\n",
    ")\n",
    "\n",
    "_ = plt.hist(params.block_delay_at_height(), stacked=True, bins=100)\n",
    "_ = plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "48c54c25-c7b4-47f9-a00a-5f10997cf185",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "network = NetworkParams(\n",
    "    mixnet_delay_mean=10, # seconds\n",
    "    mixnet_delay_var=4,\n",
    "    broadcast_delay_mean=1, # second\n",
    "    pol_proof_time=2, # seconds\n",
    ")\n",
    "\n",
    "\n",
    "mixnet_delay_data = np.array([network.sample_mixnet_delay() for _ in range(100000)])\n",
    "\n",
    "plt.figure(figsize=(16,8))\n",
    "ax = plt.subplot(221)\n",
    "_ = ax.hist(mixnet_delay_data, bins=100)\n",
    "ax.set_title(f\"mixnet delay\")\n",
    "_ = ax.set_ylabel(\"frequency\")\n",
    "_ = ax.set_xlabel(\"delay (seconds)\")\n",
    "\n",
    "broadcast_delay_data = network.sample_broadcast_delay(np.zeros(100000))\n",
    "ax = plt.subplot(222)\n",
    "_ = ax.hist(broadcast_delay_data, bins=100)\n",
    "ax.set_title(f\"block broadcast_delay\")\n",
    "ax.set_ylabel(\"frequency\")\n",
    "ax.set_xlabel(\"delay (seconds)\")\n",
    "\n",
    "BLOCK_TIME = 0\n",
    "block_arrival_slots = np.array([network.block_arrival_time(np.array([BLOCK_TIME])) for _ in range(10000)])\n",
    "\n",
    "ax = plt.subplot(212)\n",
    "_ = ax.hist(block_arrival_slots, bins=100)\n",
    "ax.set_title(f\"block arrival slot when sent in slot {BLOCK_TIME}\")\n",
    "ax.set_ylabel(\"frequency\")\n",
    "ax.set_xlabel(\"arrival time\")\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "94cc80de-2c60-495f-a73a-d126717f1007",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Sim:\n",
    "    def __init__(self, params: Params, network: NetworkParams):\n",
    "        self.params = params\n",
    "        self.network = network\n",
    "        self.events = {}\n",
    "        self.blocks = []\n",
    "        self.block_heights = np.array([], dtype=np.int64)\n",
    "        self.block_arrivals = np.zeros(shape=(params.N, 0), dtype=np.int64) # arrival time to each leader for each block\n",
    "\n",
    "    def emit_block(self, t, leader, height, parent):\n",
    "        assert type(t) in [float, np.float64], type(t)\n",
    "        assert type(leader) in [int, np.int64]\n",
    "        assert type(height) in [int, np.int64]\n",
    "        assert type(parent) in [int, np.int64]\n",
    "    \n",
    "        block = Block(\n",
    "            id=len(self.blocks),\n",
    "            t=t,\n",
    "            height=height,\n",
    "            parent=parent,\n",
    "            leader=leader\n",
    "        )\n",
    "        self.blocks.append(block)\n",
    "        self.block_heights = np.append(self.block_heights, block.height)\n",
    "    \n",
    "        # decide when this block will arrive at each node\n",
    "        self.block_arrivals = np.append(self.block_arrivals, self.network.block_arrival_time(np.repeat(t, self.params.N).reshape((self.params.N, 1))), axis=1)\n",
    "        return block.id\n",
    "\n",
    "    def plot_spacetime_diagram(self, MAX_T=1 * 60 * 60):\n",
    "        alpha_index = sorted(range(self.params.N), key=lambda n: self.params.relative_stake[n])\n",
    "        nodes = [f\"$N_{n}$($\\\\alpha$={self.params.relative_stake[n]:.2f})\" for n in alpha_index]\n",
    "        messages = [(nodes[alpha_index.index(self.blocks[b].leader)], nodes[alpha_index.index(node)], self.blocks[b].t, arrival_t, f\"$B_{{{b}}}$\") for b, arrival_ts in enumerate(self.block_arrivals.T) for node, arrival_t in enumerate(arrival_ts) if arrival_t < MAX_T]\n",
    "        \n",
    "        fig, ax = plt.subplots(figsize=(8,8))\n",
    "        \n",
    "        # Plot vertical lines for each node\n",
    "        max_slot = max(s for _,_,start_t, end_t,_ in messages for s in [start_t, end_t])\n",
    "        for i, node in enumerate(nodes):\n",
    "            ax.plot([i, i], [0, max_slot], 'k-', linewidth=0.1)\n",
    "            ax.text(i, max_slot + 30 * (0 if i % 2 == 0 else 1), node, ha='center', va='bottom')\n",
    "        \n",
    "        # Plot messages\n",
    "        colors = plt.cm.rainbow(np.linspace(0, 1, len(messages)))\n",
    "        for (start, end, start_time, end_time, label), color in zip(messages, colors):\n",
    "            start_idx = nodes.index(start)\n",
    "            end_idx = nodes.index(end)\n",
    "            ax.annotate('', xy=(end_idx, end_time), xytext=(start_idx, start_time),\n",
    "                        arrowprops=dict(arrowstyle='->', color=\"black\", lw=0.5))\n",
    "            placement = 0\n",
    "            mid_x = start_idx * (1 - placement) + end_idx * placement\n",
    "            mid_y = start_time * (1 - placement) + end_time * placement\n",
    "            ax.text(mid_x, mid_y, label, ha='center', va='center', \n",
    "                    bbox=dict(facecolor='white', edgecolor='none', alpha=0.7))\n",
    "        \n",
    "        ax.set_xlim(-1, len(nodes))\n",
    "        ax.set_ylim(0, max_slot + 70)\n",
    "        ax.set_xticks(range(len(nodes)))\n",
    "        ax.set_xticklabels([])\n",
    "        # ax.set_yticks([])\n",
    "        ax.set_title('Space-Time Diagram')\n",
    "        ax.set_ylabel('Time')\n",
    "        \n",
    "        plt.tight_layout()\n",
    "        plt.show()\n",
    "\n",
    "    def honest_chain(self):\n",
    "        chain_head = max(self.blocks, key=lambda b: b.height)\n",
    "        honest_chain = {chain_head.id}\n",
    "        \n",
    "        curr_block = chain_head\n",
    "        while curr_block.parent >= 0:\n",
    "            honest_chain.add(curr_block.parent)\n",
    "            curr_block = self.blocks[curr_block.parent]\n",
    "        return sorted(honest_chain, key=lambda b: self.blocks[b].height)\n",
    "\n",
    "    def visualize_chain(self):\n",
    "        honest_chain = self.honest_chain()\n",
    "        print(\"Honest chain length\", len(honest_chain))\n",
    "        honest_chain_set = set(honest_chain)\n",
    "        \n",
    "        layout = Layout()\n",
    "        layout.hierachical = True\n",
    "        \n",
    "        G = Network(width=1600, height=800, notebook=True, directed=True, layout=layout, cdn_resources='in_line')\n",
    "\n",
    "        for block in self.blocks:\n",
    "            # level = slot\n",
    "            level = block.height\n",
    "            color = \"lightgrey\"\n",
    "            if block.id in honest_chain_set:\n",
    "                color = \"orange\"\n",
    "\n",
    "            G.add_node(int(block.id), level=block.height, color=color, label=f\"{block.t:.2f}\")\n",
    "            # G.add_node(int(block.id), level=block.t * 0.1, color=color, label=f\"{block.height}\")\n",
    "\n",
    "            if block.parent >= 0:\n",
    "                G.add_edge(int(block.id), int(block.parent), width=2, color=color)\n",
    "        \n",
    "        return G.show(\"chain.html\")\n",
    "\n",
    "    def adverserial_analysis(self):\n",
    "        np.random.seed(0)\n",
    "        adversary = self.params.N - 1\n",
    "        \n",
    "        reorg_depths = []\n",
    "        honest_chain = self.honest_chain()\n",
    "        print(\"honest_chain length\", len(honest_chain))\n",
    "\n",
    "        adversary_delays = self.delays.T[adversary]\n",
    "\n",
    "        for block in self.blocks:\n",
    "            if block.id % 100 == 0:\n",
    "                print(\"processing\", block)\n",
    "            nearest_honest_block = block\n",
    "            while nearest_honest_block.height >= len(honest_chain) or honest_chain[nearest_honest_block.height-1] != nearest_honest_block.id:\n",
    "                nearest_honest_block = self.blocks[nearest_honest_block.parent]\n",
    "        \n",
    "            \n",
    "            adversary_blocks = []\n",
    "            t = block.t\n",
    "            for h in range(block.height + 1, self.params.CHAIN_HEIGHT):\n",
    "                t += adversary_delays[h-1]\n",
    "                adversary_blocks.append(t)\n",
    "                adverserial_height = block.height + len(adversary_blocks)\n",
    "                \n",
    "                honest_chain_up_to_t = [\n",
    "                    b for b in honest_chain\n",
    "                    if self.blocks[b].t <= t\n",
    "                ]\n",
    "                last_honest_block = self.blocks[honest_chain_up_to_t[-1]]\n",
    "                assert last_honest_block.height >= nearest_honest_block.height, (t, last_honest_block, nearest_honest_block)\n",
    "                if last_honest_block.height < adverserial_height:\n",
    "                    reorg_depths += [last_honest_block.height - nearest_honest_block.height]\n",
    "        \n",
    "        plt.hist(reorg_depths, bins=60)\n",
    "        plt.grid(True)\n",
    "        plt.title(f\"reorg depths with {self.params.adversary_control * 100:.0f}% adversary\")\n",
    "        plt.show()\n",
    "\n",
    "    def run(self, seed=None):\n",
    "        if seed is not None:\n",
    "            np.random.seed(seed)\n",
    "\n",
    "        \n",
    "        # emit the genesis block\n",
    "                \n",
    "        \n",
    "        t = 0.0\n",
    "        self.emit_block(\n",
    "            t=t,\n",
    "            leader=0,\n",
    "            height=1,\n",
    "            parent=-1,\n",
    "        )\n",
    "        self.block_arrivals[:,:] = 0 # all nodes see the genesis block immediately\n",
    "        \n",
    "        self.delays = self.params.block_delay_at_height()\n",
    "\n",
    "        for h in range(1, self.params.CHAIN_HEIGHT):\n",
    "            for leader, block_delay in enumerate(self.delays[h-1]):\n",
    "                if self.params.adversary_control and leader == self.params.N-1:\n",
    "                    continue\n",
    "                leader_arrivals = self.block_arrivals[leader]\n",
    "                \n",
    "                parent = (leader_arrivals == leader_arrivals[self.block_heights == h].min()).argmax()\n",
    "                assert parent is not None\n",
    "                assert self.blocks[parent].height == h, (self.blocks[parent], h)\n",
    "                self.emit_block(\n",
    "                    t=self.blocks[parent].t + block_delay,\n",
    "                    leader=leader,\n",
    "                    height=self.blocks[parent].height + 1,\n",
    "                    parent=parent,\n",
    "                )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "617a5279-43cb-4fb2-ae65-33fa3a5355fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avg blocks per sec 0.21317693308797184\n",
      "Number of blocks 2441\n",
      "longest chain 245\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "sim = Sim(\n",
    "    params=Params(\n",
    "        CHAIN_HEIGHT=245,\n",
    "        MEAN_BLOCK_TIME=20,\n",
    "        honest_stake = np.random.pareto(10, size=10),\n",
    "        adversary_control=0.3,\n",
    "    ),\n",
    "    network=NetworkParams(\n",
    "        mixnet_delay_mean=10, # seconds\n",
    "        mixnet_delay_var=4,\n",
    "        broadcast_delay_mean=2, # second\n",
    "        pol_proof_time=2, # seconds\n",
    "    )\n",
    ")\n",
    "sim.run(seed=5)\n",
    "# sim.visualize_chain()\n",
    "# sim.plot_spacetime_diagram()\n",
    "\n",
    "n_blocks_per_s = len(sim.blocks) / max(b.t for b in sim.blocks)\n",
    "print(\"avg blocks per sec\", n_blocks_per_s)\n",
    "print(\"Number of blocks\", len(sim.blocks))\n",
    "print(\"longest chain\", max(b.height for b in sim.blocks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d6ecc3ce-9206-4e0b-9118-55cc01aea8fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "honest_chain length 245\n",
      "processing Block(id=0, t=0.0, height=1, parent=-1, leader=0)\n",
      "processing Block(id=100, t=1231.1825397618154, height=11, parent=81, leader=9)\n",
      "processing Block(id=200, t=643.888657267845, height=21, parent=189, leader=9)\n",
      "processing Block(id=300, t=2018.0763488312223, height=31, parent=286, leader=9)\n",
      "processing Block(id=400, t=1652.7268466796731, height=41, parent=390, leader=9)\n",
      "processing Block(id=500, t=2166.111823344706, height=51, parent=483, leader=9)\n",
      "processing Block(id=600, t=2309.4070586513462, height=61, parent=588, leader=9)\n",
      "processing Block(id=700, t=1975.9198897321473, height=71, parent=689, leader=9)\n",
      "processing Block(id=800, t=2166.04768532737, height=81, parent=787, leader=9)\n",
      "processing Block(id=900, t=2480.0230869739353, height=91, parent=882, leader=9)\n",
      "processing Block(id=1000, t=4488.3970031230565, height=101, parent=986, leader=9)\n",
      "processing Block(id=1100, t=3511.4998241967496, height=111, parent=1083, leader=9)\n",
      "processing Block(id=1200, t=5101.30605009875, height=121, parent=1189, leader=9)\n",
      "processing Block(id=1300, t=4461.73775749359, height=131, parent=1288, leader=9)\n",
      "processing Block(id=1400, t=4971.418138581639, height=141, parent=1388, leader=9)\n",
      "processing Block(id=1500, t=5558.756693373566, height=151, parent=1488, leader=9)\n",
      "processing Block(id=1600, t=5666.4009766452255, height=161, parent=1582, leader=9)\n",
      "processing Block(id=1700, t=5619.044916466169, height=171, parent=1689, leader=9)\n",
      "processing Block(id=1800, t=5806.723632336016, height=181, parent=1788, leader=9)\n",
      "processing Block(id=1900, t=8114.93522758204, height=191, parent=1889, leader=9)\n",
      "processing Block(id=2000, t=6222.034399400075, height=201, parent=1987, leader=9)\n",
      "processing Block(id=2100, t=6611.0363127282435, height=211, parent=2089, leader=9)\n",
      "processing Block(id=2200, t=6841.239918856918, height=221, parent=2189, leader=9)\n",
      "processing Block(id=2300, t=7713.936866630708, height=231, parent=2288, leader=9)\n",
      "processing Block(id=2400, t=8046.790543317015, height=241, parent=2385, leader=9)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim.adverserial_analysis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "89bf9a0f-7f47-4216-80e8-5e6e24998f3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'PoL time as fraction of mean block time')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "net_params = [NetworkParams(\n",
    "        mixnet_delay_mean=0.1, # seconds\n",
    "        mixnet_delay_var=0.1,\n",
    "        broadcast_delay_mean=0.1, # second\n",
    "        pol_proof_time=i/N * 5, # seconds\n",
    "    ) for i in range(N)]\n",
    "\n",
    "sims = [Sim(\n",
    "    params=Params(\n",
    "        CHAIN_HEIGHT=1000, # seconds\n",
    "        MEAN_BLOCK_TIME=20,\n",
    "        honest_stake = np.random.pareto(10, size=10),\n",
    "        adversary_control=0.1,\n",
    "    ),\n",
    "    network=net\n",
    ") for net in net_params]\n",
    "\n",
    "[sim.run() for sim in sims]\n",
    "\n",
    "\n",
    "plt.scatter([sim.network.pol_proof_time / sim.params.MEAN_BLOCK_TIME for sim in sims], [100 - 100 * len(sim.honest_chain()) / len(sim.blocks) for sim in sims])\n",
    "plt.ylabel(\"wasted blocks %\")\n",
    "plt.xlabel(\"PoL time as fraction of mean block time\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c21cfba-68b3-487b-a273-76776defddca",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}